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Example 1.
We use the Retrieve command to obtain a Lie algebra of vector fields in the paper by Gonzalez-Lopez, Kamran, and Olver from the DifferentialGeometry Library. We compute the isotropy subalgebra and isotropy representation at the points and
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M >
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| (2.1) |
M >
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| (2.2) |
Alg1 >
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We illustrate some different possible outputs from the IsotropySubalgebra program.
Alg1 >
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| (2.4) |
M >
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| (2.5) |
Alg1 >
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Alg1 >
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| (2.6) |
Alg1 >
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Note that the vectors in Iso2 all vanish at
It is apparent from the multiplication table that the pair Alg1, S1 is a symmetric pair with respect to the complementary subspace. We can check this with the command Query/"SymmetricPair".
Alg1 >
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The linear isotropy representation can be converted to a representation.
Alg1 >
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| (2.8) |
iso1 >
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iso1 >
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